Mr Flynn has reportedly offered to cooperate with FBI investigators and two Congressional committees in return for immunity from prosecution, as they probe Russia's alleged cyber-meddling in the 2016 election, and possible links between Moscow and Mr Trump’s campaign team.

On Friday morning, Mr Trump tweeted his belief that Mr Flynn should indeed testify. “Mike Flynn should ask for immunity in that this is a witch hunt (excuse for big election loss), by media & Dems, of historic proportion.

Mr Trump would not comment further when asked about Mr Flynn during a White House meeting with US manufacturers.

However, White House spokesman Sean Spicer later doubled down on this at a briefing with reporters. Asked if Mr Trump was concerned about possible testimony from Mr Flynn, he replied: “Nope.”

“He believes that Mike Flynn should go testify,” Mr Spicer said. “He should go up there and do what he has to do to get the story out.”

Asked whether it was appropriate for Mr Flynn to seek immunity - something both Mr Trump and Mr Flynn had previously suggested was evidence of criminal behaviour - he said: “That is up to him and his lawyer. I’m not going to give Mike Flynn or anyone else legal advice from the podium.”

Mr Spicer said Mr Trump wanted Mr Flynn to testify to “get this matter behind us” but declined to say specifically that he should be granted immunity.

“The president is very clear that he wants Mike Flynn to go and be completely open and transparent with the committee, and whatever it takes to do that he is supportive of,” Mr Spicer said.

Meanwhile, Congressional investigators on Friday rebuffed Mr Flynn’s offer of cooperation in exchange for immunity from prosecution, saying it is too early in their probe of possible Russia connections to discuss a deal.

The Associated Press said a congressional aide confirmed that preliminary discussions with the Senate intelligence committee involved immunity but that it was too early in the investigation to set terms.

The top Democrat on the House Intelligence Committee, Congressman Adam Schiff, of California, said committee leaders would be discussing the issue with their Senate counterparts and the Justice Department.

“We should first acknowledge what a grave and momentous step it is for a former national security adviser to the president of the United States to ask for immunity from prosecution,” Mr Schiff said in a statement.

“As with any investigation - and particularly one that grows in severity and magnitude by the day - there is still much work and many more witnesses and documents to obtain before any immunity request from any witness can be considered,” Mr Schiff said.

Mr Schiff went to the White House on Friday at the administration's invitation to review documents that it said support Trump's contention he and his team were subjected to surveillance by the Obama administration during the presidential campaign.

Mr Flynn’s lawyer, Robert Kelner, said no “reasonable person” who has a lawyer would answer questions without assurances that he would not be prosecuted, given calls from some members of Congress that the retired lieutenant general should face criminal charges.

“General Flynn certainly has a story to tell, and he very much wants to tell it, should the circumstances permit,” Mr Kelner said

The Republican chairman of the House Intelligence Committee, Devin Nunes, has been criticised by his colleagues on the panel for his handling of the investigation of possible Russian connections, including going to the White House complex independently to review documents on the purported surveillance.

FBI Director James Comey has said there is no evidence of wiretapping at Trump Tower in New York but that the agency is investigating whether the Trump campaign colluded with Russia.

Senator Angus King, a member of the Senate Intelligence Committee, also said it was too soon to discuss immunity.

Mr Flynn was forced to resign on 13 February for failing to disclose talks with Russian ambassador to the US, Sergei Kislyak about US sanctions on Moscow and misleading Vice President Mike Pence about the conversations, which occurred before Trump took office

The Russian government has denied the allegations and denied that it hacked emails of Democratic groups and released information to tip the election toward Trump, who has called for better U.S. relations with Moscow.

In a CNN interview on Friday, Mr King defended the investigations. “This is not a witch hunt... This is an effort to get to the truth of some very important questions.

“There is no doubt whatsoever that the Russians were behind an effort to interfere in our elections,” Mr King said. “To continue to deny that - it just flies in the face of all of the reality.”​